Question

Why is $\lim_{x\to a}{[f(x)\cdot g(x)]}=\lim_{x\to a}{f(x)}\cdot\lim_{x\to a}{g(x)}$, but $(fg)' = f'g+fg'$

score 100 · Answer 1 · 2026-04-18 09:57:03

100

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Why is $\lim_{x\to a}{[f(x)\cdot g(x)]}=\lim_{x\to a}{f(x)}\cdot\lim_{x\to a}{g(x)}$, but $(fg)' = f'g+fg'$

Published on 18 Apr 2026 - 9:57

score 164 · Answer 2 · 2026-04-26 00:22:24

164

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Directional Derivatives - Multivariable Calculus

Published on 26 Apr 2026 - 0:22

score 146 · Answer 3 · 2026-04-15 19:51:24

146

Views

Find integral of $\int\frac{\tan x}{\sqrt{\cos^4x-1}}$

Published on 15 Apr 2026 - 19:51

score 88 · Answer 4 · 2026-04-13 12:57:22

88

Views

Applications of Derivatives;Fabricating a Box

Published on 13 Apr 2026 - 12:57

score 41 · Answer 5 · 2026-04-10 20:46:06

41

Views

How can I write explicit expressions for gradients and derivatives about a given function?

Published on 10 Apr 2026 - 20:46

score 500 · Answer 6 · 2026-04-14 12:35:59

500

Views

Why $g$ is not monotonic in any neighborhood of $0?$

Published on 14 Apr 2026 - 12:35

score 2.1k · Answer 7 · 2026-04-09 02:35:03

2.1k

Views

How to derive the growth rate rules from the log growth equation?

Published on 09 Apr 2026 - 2:35

score 446 · Answer 8 · 2026-04-23 11:28:59

446

Views

Prob. 20 (a) & (b), Exercises 8.9, in Apostol's CALCULUS vol. 2: If $f^\prime(x;y)=0$ for every $x$ and for every $y$, . . .

Published on 23 Apr 2026 - 11:28

score 44 · Answer 9 · 2026-04-12 06:04:09

44

Views

Derivative of an equation, math

Published on 12 Apr 2026 - 6:04

score 311 · Answer 10 · 2026-04-13 17:01:36

311

Views

Using the limit definition to find a derivative for $\frac{-5x}{2+\sqrt{x+3}}$

Published on 13 Apr 2026 - 17:01

score 18.5k · Answer 11 · 2026-04-14 14:06:54

18.5k

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Derivative of product of matrix by vector

Published on 14 Apr 2026 - 14:06

score 2.1k · Answer 12 · 2026-04-15 12:43:14

2.1k

Views

Proving $\sum_{n=1}^{\infty}\frac{(-1)^{n-1}}{2n-1}x^{2n-1}$ is differentiable

Published on 15 Apr 2026 - 12:43

score 53 · Answer 13 · 2026-04-13 20:20:01

53

Views

Compute derivative of $\frac{f(z)}{f'(z)}$ at a root of $f(z)$.

Published on 13 Apr 2026 - 20:20

score 383 · Answer 14 · 2026-04-08 15:38:22

383

Views

Differentiate an exponential operator

Published on 08 Apr 2026 - 15:38

score 262 · Answer 15 · 2026-04-10 17:49:11

262

Views

Reconcile the chain rule with a derivative formula

Published on 10 Apr 2026 - 17:49

List Question

Why is $\lim_{x\to a}{[f(x)\cdot g(x)]}=\lim_{x\to a}{f(x)}\cdot\lim_{x\to a}{g(x)}$, but $(fg)' = f'g+fg'$

Directional Derivatives - Multivariable Calculus

Find integral of $\int\frac{\tan x}{\sqrt{\cos^4x-1}}$

Applications of Derivatives;Fabricating a Box

How can I write explicit expressions for gradients and derivatives about a given function?

Why $g$ is not monotonic in any neighborhood of $0?$

How to derive the growth rate rules from the log growth equation?

Prob. 20 (a) & (b), Exercises 8.9, in Apostol's CALCULUS vol. 2: If $f^\prime(x;y)=0$ for every $x$ and for every $y$, . . .

Derivative of an equation, math

Using the limit definition to find a derivative for $\frac{-5x}{2+\sqrt{x+3}}$

Derivative of product of matrix by vector

Proving $\sum_{n=1}^{\infty}\frac{(-1)^{n-1}}{2n-1}x^{2n-1}$ is differentiable

Compute derivative of $\frac{f(z)}{f'(z)}$ at a root of $f(z)$.

Differentiate an exponential operator

Reconcile the chain rule with a derivative formula

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